➕ ADD: altogether, in total, combined
➖ SUBTRACT: how much more, left, remaining
✖️ MULTIPLY: "of," each, part of a part, area
➗ DIVIDE: shared equally, how many groups, how many fit
Fraction Operations
Add, Subtract, Multiply, Divide — Comprehensive Review for SBA Prep
📚
Subject
Math
⏱️
Duration
60+ min
🎯
Standard
5.NF.A.1
📋 Standards & Objectives
📜Standards
5.NF.A.1Add and subtract fractions with unlike denominators (including mixed numbers).
5.NF.A.2Solve word problems involving addition and subtraction of fractions.
5.NF.B.4Multiply a fraction or whole number by a fraction.
5.NF.B.6Solve real-world problems involving multiplication of fractions and mixed numbers.
5.NF.B.7Divide unit fractions by whole numbers and whole numbers by unit fractions.
🎯SWBAT
- Identify which fraction operation to use based on context clues in word problems.
- Add and subtract fractions with unlike denominators by finding a common denominator.
- Multiply fractions (including whole numbers) and interpret the result.
- Divide with unit fractions and solve all four fraction operation types in SBA format.
📖 Key Vocabulary
📝Common Denominator
A shared multiple of two or more denominators. You need a common denominator before you can add or subtract fractions.
To add 14 + 13, find a common denominator: 12. Rewrite as 312 + 412.
The common denominator of 6 and 8 is 24 — that's the smallest number both 6 and 8 divide into evenly.
📝Reciprocal
The fraction you get when you flip the numerator and denominator. Used when dividing fractions ("Keep, Change, Flip").
The reciprocal of 14 is 41 (which equals 4).
The reciprocal of 35 is 53. Multiply by the reciprocal instead of dividing!
📝Numerator
The top number in a fraction — it tells how many parts you have.
In 34, the numerator is 3 — you have 3 out of 4 equal parts.
When you multiply fractions, multiply the numerators together: 23 × 45 → top: 2 × 4 = 8.
📝Key Words
Specific words in a word problem that signal which operation to use. Key words are your biggest clue on the SBA.
"Altogether" and "in total" are key words for ADDITION.
"How much more" and "remaining" are key words for SUBTRACTION. "Of" usually means MULTIPLY.
📝Simplify
To reduce a fraction to its smallest equivalent form by dividing the numerator and denominator by their greatest common factor.
Simplify 68: divide both by 2 → 34. Same amount, smaller numbers!
Always simplify your final answer on the SBA — scorers want to see the simplest form.
🚀 The Big Challenge
Can you figure out the operation?
Four Operations. One Skill.
Today we're putting ALL your fraction skills together. The SBA won't tell you "add these fractions" — it gives you a word problem and YOU decide the operation.
The #1 mistake on the SBA? Picking the WRONG operation.
By the end of today, you'll be able to read ANY fraction word problem and know exactly what to do.
💡 Test-Taking Tip
SBA TIP #14
💡 CIRCLE THE KEY WORDS
➕ ADD: "altogether," "in total," "combined," "how much…and…"
➖ SUBTRACT: "how much more," "how much left," "remaining," "difference"
✖️ MULTIPLY: "of," "each," "part of a part," "area"
➗ DIVIDE: "shared equally," "how many groups," "how many fit"
How to use it: Circle these words BEFORE you do any math — they tell you the operation.
🔥 Spiral Warm-Up
Review — No fractions yet!
1️⃣Multi-Digit Division
2,156 ÷ 49 = ?
Show your work!
49 × 40 = 1,960
2,156 − 1,960 = 196
49 × 4 = 196
2,156 ÷ 49 = 44
2️⃣Powers of 10
0.065 × 104 = ?
Move the decimal!
104 = 10,000 → move decimal 4 places right
0.065 → 0.65 → 6.5 → 65 → 650
🔥 Spiral Warm-Up
Problem 3 — Volume
3️⃣Find the Base Area
A rectangular prism has:
V = 360 cm³, h = 12 cm
What is B (the base area)?
V = B × h
360 = B × 12
B = 360 ÷ 12
B = 30 cm²
🔄 Let's Switch Gears
✅ What we just reviewed:
Division, powers of 10, and volume — skills from earlier units.
⬇️ What's coming next:
ALL FOUR fraction operations — and how to know which one to use.
📋 How Do I Know Which Operation?
Anchor Chart — Your cheat sheet!
➕ADD Fractions
Combining amounts
Key words: "altogether," "in total," "combined," "how much…and…"
➖SUBTRACT Fractions
Finding differences
Key words: "how much more," "how much left," "remaining," "difference"
✖️MULTIPLY Fractions
Fraction OF a number, area, scaling
Key words: "of," "each," "part of a part," "area"
➗DIVIDE Fractions
Sharing/splitting, "how many fit"
Key words: "shared equally," "how many groups," "how many ___ fit in ___"
📓 Copy this anchor chart into your notebook!
📓 Write This Down
Operation Key Words
Key Terms
➕ Add
➖ Subtract
✖️ Multiply
➗ Divide
In Your Notebook
👨🏫 Name That Operation!
Problem 1 — Read, identify, then we'll check
"Sam ate 25 of a pizza. Tina ate 13 of the same pizza. How much did they eat altogether?"
Which operation? 🤔
➕ ADDITION
The key word "altogether" means we're combining two amounts.
👨🏫 Name That Operation!
Problem 2
"A rope is 78 of a meter. You cut off 14 of a meter. How much is left?"
Which operation? 🤔
➖ SUBTRACTION
The key word "left" means we're finding what remains after removing a part.
👨🏫 Name That Operation!
Problem 3
"A garden is 34 acre. You plant flowers in 23 of it. How much is planted?"
Which operation? 🤔
✖️ MULTIPLICATION
The key word "of" means we're finding a fraction of a fraction — that's multiplication.
👨🏫 Name That Operation!
Problem 4
"You have 3 cups of sugar. Each batch of cookies needs 14 cup. How many batches can you make?"
Which operation? 🤔
➗ DIVISION
"How many batches" = how many groups of 14 fit in 3. That's division: 3 ÷ 14 = 12 batches.
💬 Turn & Talk
🤔Discuss with a Partner
Which key word was the HARDEST to spot? Which operation do you mix up the most?
Sentence starter: "I sometimes mix up ___ and ___ because ___"
🎯 Wrong Answer Analysis
Marcus vs. Tina — Who picked the right operation?
"A rope is 78 of a meter. You cut off 14 of a meter. How much is left?"
Marcus's Setup
78 × 14
"I saw 'of a meter' so I multiplied."
Tina's Setup
78 − 14
"'How much is left' means subtract."
✅ Tina is correct!
"How much is left" is a subtraction clue. Marcus got tripped up because "of a meter" isn't a multiplication signal — it's just the unit. The word "of" only signals multiplication when it means "a fraction OF something" (like "23 of the garden").
💪 Section 2: Solve It!
Mixed Practice — All Four Operations
Time to Compute
Now that you can identify the operation, let's practice solving. We'll work through addition, subtraction, multiplication, and division — with visual models for each.
👨🏫 ➕ Addition: I Do
Find a common denominator, then add
34 + 25 = ?
1 Find the common denominator: LCD of 4 and 5 = 20
2 Rewrite: 3 × 54 × 5 = 1520 2 × 45 × 4 = 820
3 Add numerators: 15 + 820 = 2320
✓ 2320 = 1320
34
25
👥 ➕ Addition: We Do
Word Problem — Find the key words
"You drank 13 of a gallon of water in the morning and 25 of a gallon in the afternoon. How much total?"
1 Operation: "total" = ➕ ADD
2 Common denominator of 3 and 5 = 15
3 515 + 615 = 1115
✓ 1115 of a gallon
👨🏫 ➖ Subtraction: I Do
Same idea — common denominator first!
56 − 38 = ?
1 LCD of 6 and 8 = 24
2 5 × 46 × 4 = 2024 3 × 38 × 3 = 924
3 Subtract numerators: 20 − 924 = 1124
✓ 1124
👥 ➖ Subtraction: We Do
Word Problem
"Kara had 34 of a pound of clay. She used 13 of a pound. How much is left?"
1 Operation: "left" = ➖ SUBTRACT
2 Common denominator of 4 and 3 = 12
3 912 − 412 = 512
✓ 512 of a pound left
✅ Quick Check
True or False?
When you add or subtract fractions, you need a common denominator — but when you multiply, you do NOT.
👍 Thumbs up if TRUE 👎 Thumbs down if FALSE
👍 TRUE!
Add/subtract → need a common denominator. Multiply → just multiply straight across (numerator × numerator, denominator × denominator).
👨🏫 ✖️ Multiplication: I Do
Multiply straight across — no common denominator needed!
35 × 47 = ?
1 Multiply numerators: 3 × 4 = 12
2 Multiply denominators: 5 × 7 = 35
✓ 1235
Area Model: 5 columns × 7 rows = 35 total squares. Shade 3 columns × 4 rows = 12 squares.
👥 ✖️ Multiplication: We Do
Fraction OF a whole number
"23 of the 36 students finished early. How many finished early?"
1 Operation: "of" = ✖️ MULTIPLY
2 Set up: 23 × 361
3 2 × 363 = 723 = 24
✓ 24 students finished early
👨🏫 ➗ Division: I Do
Keep, Change, Flip — use the reciprocal!
6 ÷ 13 = ?
1 Keep the first number: 6
2 Change ÷ to ×
3 Flip the second fraction (reciprocal): 13 → 31
4 6 × 31 = 181 = 18
✓ 6 ÷ 13 = 18
Visual: How many 13 pieces fit in 6 wholes?
6 wholes × 3 thirds each = 18 pieces!
👥 ➗ Division: We Do
Word Problem — sharing a fraction
"12 of a cake is shared equally among 5 kids. What fraction does each kid get?"
1 Operation: "shared equally" = ➗ DIVIDE
2 Set up: 12 ÷ 5
3 Keep, Change, Flip: 12 × 15
4 1 × 12 × 5 = 110
✓ Each kid gets 110 of the cake
📓 Write This Down
All Four Fraction Operations
Operations
➕ Add/Sub
✖️ Multiply
➗ Divide
The Rules
➕➖ Add/Subtract: Find a common denominator, rewrite both fractions, then add or subtract the numerators. Keep the denominator.
✖️ Multiply: Multiply numerators × numerators. Multiply denominators × denominators. Simplify.
➗ Divide: Keep the first fraction, change ÷ to ×, flip the second fraction (reciprocal). Then multiply.
✖️ Multiply: Multiply numerators × numerators. Multiply denominators × denominators. Simplify.
➗ Divide: Keep the first fraction, change ÷ to ×, flip the second fraction (reciprocal). Then multiply.
🔄 Level Up!
✅ What we just practiced:
Each operation separately — add, subtract, multiply, divide.
⬇️ What's coming next:
Mixed problems — YOU decide the operation. No hints!
🔍 Mixed Challenge #1
🧠 YOU pick the operation, then solve
"Maria ran 34 mile on Monday and 56 mile on Tuesday. How much farther did she run on Tuesday?"
1 Operation: "how much farther" = ➖ SUBTRACT
2 56 − 34 → LCD = 12
3 1012 − 912 = 112
✓ Maria ran 112 mile farther on Tuesday
🔍 Mixed Challenge #2
🧠 YOU pick the operation, then solve
"A farm has 48 animals. 512 of them are chickens. How many chickens?"
1 Operation: "fraction of a number" = ✖️ MULTIPLY
2 512 × 48 = 5 × 4812 = 24012
✓ 240 ÷ 12 = 20 chickens
🔍 Mixed Challenge #3
🧠 YOU pick the operation, then solve
"It takes 15 of a bag of soil per pot. You have 8 bags. How many pots can you fill?"
1 Operation: "How many [unit fractions] fit" = ➗ DIVIDE
2 8 ÷ 15 → Keep, Change, Flip → 8 × 51
✓ 8 × 5 = 40 pots
🔍 Mixed Challenge #4
🧠 YOU pick the operation, then solve
"A recipe needs 23 cup of oil. Another recipe needs 34 cup. How much oil for both recipes?"
1 Operation: "both recipes" = combining = ➕ ADD
2 23 + 34 → LCD = 12
3 812 + 912 = 1712
✓ 1512 cups of oil
💬 Turn & Talk
🤔Discuss with a Partner
Which of the 4 mixed challenge problems was the trickiest? What key word helped you decide?
Sentence starter: "Problem #___ was tricky because ___, but the key word '___' told me to ___."
🎯 SBA Spotlight
Select the correct operation for each problem
AMia's Drinks
"Mia drank 23 cup of juice and 14 cup of milk. How much liquid total?"
✅ ADD — "total" = combining amounts
BRibbon Pieces
"A 5-yard ribbon is cut into 14-yard pieces. How many pieces?"
✅ DIVIDE — "how many pieces fit" = 5 ÷ 14 = 20
CFloor Area
"A floor is 23 yd by 56 yd. What's the area?"
✅ MULTIPLY — "area" = length × width = 1018 = 59 yd²
DFraction of Students
"34 of 20 students brought lunch. How many?"
✅ MULTIPLY — "of" = fraction of a number = 34 × 20 = 15
🎯 SBA Spotlight
Constructed Response — Write your own word problems!
SBA Challenge: Write a SHORT word problem for EACH operation using fractions.
Explain what key word or context clue made you choose that operation.
Model Strong Response:
➕ ADD: "Jake walked 38 mi to school and 14 mi to the store. How far did he walk in total?" → I chose ADD because "in total" means combining distances.
➖ SUBTRACT: "A bottle had 78 liter. I drank 12 liter. How much is left?" → I chose SUBTRACT because "left" means finding what remains.
✖️ MULTIPLY: "A lot is 25 acre. 34 of it is grass. How much grass?" → I chose MULTIPLY because "of" means a fraction of something.
➗ DIVIDE: "4 pies are shared equally among 13-pie servings. How many servings?" → I chose DIVIDE because "shared equally" means splitting.
🎯 SBA-Style Practice
Multiple Choice — Watch for traps!
A recipe calls for 34 cup of flour. You want to make 23 of the recipe. How much flour do you need?
A57
❌ Added numerators and denominators directly (3+2=5, 4+3=7). Fractions don't add that way!
B✅ 612 = 12
✅ "23 of" = MULTIPLY. 34 × 23 = 612 = 12 cup
C1512
❌ Added the fractions (34 + 23) instead of multiplying. "Of" means multiply!
D118
❌ Divided instead of multiplying (34 ÷ 23 = 98). Wrong operation!
🎯 SBA-Style Practice
Constructed Response — Show your reasoning!
"Jaya has 56 of a yard of ribbon. She uses 13 of a yard to wrap a gift. How much ribbon is left?"
Write the equation AND draw a visual model. Then explain your reasoning.
1 "I know this is subtraction because 'how much is left' tells me to find the remaining amount."
2 Equation: 56 − 13 → LCD = 6 → 56 − 26 = 36
✓ Simplified: 36 = 12 yard of ribbon left
📓 Summary Note
Write 1 Sentence
In the bottom of your notebook page, write one sentence explaining how you decide which fraction operation to use in a word problem. Use at least ONE example of a key word.
🎫 Exit Ticket
Show what you know — 4 questions!
1️⃣Add Fractions
58 + 23 = ?
Show your work — find the common denominator!
LCD = 24
1524 + 1624 = 3124
1724
2️⃣Word Problem
"You have 34 gal of paint. You use 13 gal. How much is left?"
Subtract: 912 − 412
512 gallon left
3️⃣SBA: Operation ID + Solve
Write the operation (+, −, ×, ÷), then solve:
(a) A park is 56 mi × 25 mi. Area?
(b) 14 cup per feeder, 5 cups. How many feeders?
(a) ✖️ 56 × 25 = 1030 = 13 mi²
(b) ➗ 5 ÷ 14 = 5 × 4 = 20 feeders
4️⃣🔄 Spiral Review
"A cake recipe needs 34 cup of sugar. A cookie recipe needs 23 cup. How much MORE sugar does the cake need?"
Subtract: 912 − 812
112 cup more